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A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…

In the practical applications of computed tomography imaging, the projection data may be acquired within a limited-angle range and corrupted by noises due to the limitation of scanning conditions. The noisy incomplete projection data…

We present the optimal design of a spectral method widely used to initialize nonconvex optimization algorithms for solving phase retrieval and other signal recovery problems. Our work leverages recent results that provide an exact…

We consider the problem of minimizing a convex, separable, nonsmooth function subject to linear constraints. The numerical method we propose is a block-coordinate extension of the Chambolle-Pock primal-dual algorithm. We prove convergence…

We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements. In contrast to state of the art…

Nonconvex-nonconcave minimax optimization has gained widespread interest over the last decade. However, most existing works focus on variants of gradient descent-ascent (GDA) algorithms, which are only applicable to smooth nonconvex-concave…

Spectral computed tomography (CT) has attracted much attention in radiation dose reduction, metal artifacts removal, tissue quantification and material discrimination. The x-ray energy spectrum is divided into several bins, each…

Reconstruction of CT images from a limited set of projections through an object is important in several applications ranging from medical imaging to industrial settings. As the number of available projections decreases, traditional…

In this paper, we propose a new decomposition approach named the proximal primal dual algorithm (Prox-PDA) for smooth nonconvex linearly constrained optimization problems. The proposed approach is primal-dual based, where the primal step…

Computed Tomography (CT) imaging technique is widely used in geological exploration, medical diagnosis and other fields. In practice, however, the resolution of CT image is usually limited by scanning devices and great expense. Super…

The susceptibility-based positive contrast MR technique was applied to estimate arbitrary magnetic susceptibility distributions of the metallic devices using a kernel deconvolution algorithm with a regularized L-1 minimization.Previously,…

In this paper, we use Proximal Cubic regularized Newton Methods (PCNM) to optimize the sum of a smooth convex function and a non-smooth convex function, where we use inexact gradient and Hessian, and an inexact subsolver for the cubic…

Hyperspectral image (HSI) deconvolution is a challenging ill-posed inverse problem, made difficult by the data's high dimensionality.We propose a parameter-parsimonious framework based on a low-rank Canonical Polyadic Decomposition (CPD) of…

The presence of inhomogeneous media between optical sensors and objects leads to distorted imaging outputs, significantly complicating downstream image-processing tasks. A key challenge in image restoration is the lack of high-quality,…

In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…

In this paper, we investigate image reconstruction for dynamic Computed Tomography. The motion of the target with respect to the measurement acquisition rate leads to highly resolved in time but highly undersampled in space measurements.…

Deep Learning (DL) methods can reconstruct highly accelerated magnetic resonance imaging (MRI) scans, but they rely on application-specific large training datasets and often generalize poorly to out-of-distribution data. Self-supervised…

This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Computational imaging, especially non-line-of-sight (NLOS) imaging, the…

Standard dual-energy computed tomography (CT) uses two different X-ray energies to obtain energy-dependent tissue attenuation information to allow quantitative material decomposition. The combined use of dual-energy CT and positron emission…

Hyperspectral Imaging is a crucial tool in remote sensing which captures far more spectral information than standard color images. However, the increase in spectral information comes at the cost of spatial resolution. Super-resolution is a…